ON THE INTENSITY OF SOLAR lUDIATION. 161 



^=T + -+ce-«' (2) 



q ' 



Hence if u denotes the excess of temperature of the central thermometer 

 over that of the case, we see from (2), or directly from (1), that u tends 

 to the limit 



IT 



u= ~=:\r, say ..... (3) 



■when the time t which has elapsed since exposure, or whatever other 

 change it may have been in the disposition of the instrument, is large 

 enough to permit of our neglecting the last term in (2). The constant 

 X, the reciprocal of q, in (3) denotes a time, which may conveniently be 

 called the lagging time of the thermometer n. 



Were the actinometer used as a statical instrument the simple ex- 

 pression (3) is all that we should be concerned with. The quantity r 

 varies as the radiation, but involves a coefficient depending on the par- 

 ticular instrument and for a given instrument on the area of the dia- 

 phragm used, and on the presence or absence of the quartz plate which 

 is furnished for covering the aperture. The constant q need not be 

 determined, as it is associated with a coefficient depending on the instru- 

 ment. By itself alone the actinometer gives only the ratio of variation 

 of the radiation. To obtain an absolute measure the actinometer would 

 have to be compared, once for all, with some actinometer which gives 

 absolute results. We believe that the main object which Stewart had in 

 view was to furnish an instrument which might supply a means of 

 detecting possible variations in the intrinsic intensity of radiation from 

 the sun, corresponding, suppose, to the sun-spot period ; and for this 

 object the same instrument would be employed throughout, so that we 

 should not be concerned with absolute measures. 



In studying, however, the march of thermometer D when the instru- 

 ment is exposed, or else the sun's rays cut off", we must have recourse to 

 equation (2), and now we can no longer dispense with a knowledge of 

 the value of the constant q. The easiest way of determining it seemed 

 to be to make use in the first instance of the readings in the latter 

 portion of the observation, when thermometer D, after having been 

 heated by exposure, was cooling in consequence of the sun's rays having 

 been intercepted by a screen. In this case r=0, and we have simply 

 ^^°°^(2) ^_^^_,, (4^ 



Hence, if we plot the observations, taking the time for abscissa and the 

 logarithm of the excess u for ordinate, we ought to get a series of points 

 lying in a straight line. 



On laying down the observations on paper it was found that, after a 

 slight initial irregularity, the dots representing the observations lay 

 extremely closely in a straight line until the excess u, which began at 

 49°-7, was reduced to about 3°. They then began to fall a little too 

 high, and the height above the straight line representing the previous 

 observations kept increasing as we proceeded. We have not investigated 

 the cause of this variation, but it seems possible that it may have been 

 due to a slight lagging of the case thermometers. As these were still 

 rising, though D was falling, the lagging would make the temperature of 

 the case appear a little too low, and therefore the excess u a little too 

 great, and therefore the actual reduction of ti, would be somewhat less 



1892. M 



